An arc plasma simulation method based on a self-learning network architecture

Abstract

The application belongs to the technical field of plasma simulation, and discloses an arc plasma simulation method based on a self-learning network architecture, which comprises the following steps: defining a simulation process with the spatial coordinates and time of the arc plasma as input and the physical field variables determined by the arc plasma control equation as output; constructing a loss function according to the arc plasma control equation, which is used to measure the degree to which the physical field variables satisfy the control equation; taking the loss function as the standard for measuring the performance of the network architecture, constructing a discrete learning space for learning the network architecture, and introducing learnable continuous architecture parameters to continuously relax the discrete learning space to obtain a differentiable learning space; the method effectively solves the problem that the simulation method in the prior art excessively relies on artificial experience in the design of the neural network architecture and lacks effective guidance, which leads to the difficulty in obtaining an optimal network structure and easily causes the problems of insufficient simulation precision and generalization ability.

Description

Technical Field

[0001] This invention belongs to the field of plasma simulation technology, specifically relating to an arc plasma simulation method based on a self-learning network architecture. Background Technology

[0002] Arc plasma is an electrically neutral substance composed of charged and neutral particles, and it has wide applications in industry. Due to limitations in extreme experimental environments and measurement conditions, numerical simulation is the main means of studying the characteristics and mechanisms of arc plasma. Traditional numerical simulation methods usually treat arc plasma as a fluid macroscopically, and obtain the state of arc plasma by coupling and solving physical fields such as electric field, magnetic field, fluid field, and temperature field. However, traditional numerical simulation relies on numerical calculation techniques such as the finite volume method and finite element method, which have difficulties in mesh generation and equation discretization when dealing with such problems, and cannot effectively support complex arc plasma simulations.

[0003] With the advancement of artificial intelligence technology, some deep learning-based methods for simulating electric arc plasma have emerged. While these methods can avoid the processes of mesh generation and high-order equation discretization, simplifying the simulation process, they suffer from several drawbacks. First, they rely on large amounts of data for training, and acquiring relevant data for electric arc plasma is difficult and costly. Second, the design of deep neural network architectures depends on expert experience and repeated trial and error, lacking automated and structured search mechanisms. This makes it difficult to adapt to the multi-scale and strongly nonlinear solution requirements of electric arc plasma, resulting in weak model generalization ability and low computational efficiency. Therefore, existing simulation methods suffer from the problem of excessive reliance on human experience in neural network architecture design and a lack of effective guidance, making it difficult to obtain the optimal network structure and easily leading to insufficient simulation accuracy and generalization ability. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide an arc plasma simulation method based on a self-learning network architecture. This method solves the problem that existing simulation methods rely too heavily on human experience in neural network architecture design and lack effective guidance, making it difficult to obtain the optimal network structure and resulting in insufficient simulation accuracy and generalization ability.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] An arc plasma simulation method based on a self-learning network architecture includes the following steps:

[0007] The simulation process is defined with the spatial coordinates and time of the electric arc plasma as input and the physical field variables determined by the electric arc plasma control equation as output.

[0008] A loss function is constructed based on the control equations of electric arc plasma to measure the degree to which physical field variables satisfy the control equations.

[0009] Using the loss function as a standard to measure the performance of the network architecture, a discrete learning space for learning the network architecture is constructed, and learnable continuous architecture parameters are introduced to continuously relax the discrete learning space to obtain a differentiable learning space.

[0010] With minimizing the loss function as the optimization objective, a two-layer optimization method is used to jointly optimize the continuous architecture parameters in the differentiable learning space and the network weight parameters of the network architecture itself, so as to obtain the optimal continuous architecture parameters.

[0011] Based on the optimal continuous architecture parameters, the optimal network architecture in the discrete learning space is determined;

[0012] Initialize the network weight parameters of the determined optimal network architecture, and train the optimal network architecture with the goal of minimizing the loss function;

[0013] The simulation process is executed using the optimal network architecture after training. By inputting spatial coordinates and time, the corresponding physical field variables are output to obtain the simulation results of electric arc plasma.

[0014] The discrete learning space includes a variety of candidate network architectures, which are formed by combinations of different numbers of hidden layers and different numbers of neurons within each hidden layer.

[0015] Introducing learnable continuous architecture parameters to continuously relax the discrete learning space, specifically including:

[0016] Assign optimizable continuous architecture parameters to the network architecture for each configuration in the discrete learning space;

[0017] Generate a tensor mask consisting of 1s and 0s for the hidden layer in each network architecture configuration;

[0018] The continuous architecture parameters are converted into architecture selection weights for the corresponding tensor mask using differentiable functions;

[0019] Based on the architecture selection weights, the outputs of each masked network architecture are weighted and combined to generate a continuously differentiable hidden layer output representation, thus completing the continuous relaxation process.

[0020] The weighted combination of the masked network architecture outputs based on architecture selection weights is performed through architecture approximation units, specifically including:

[0021] The tensor mask is multiplied by the computation result of the hidden layer with the largest number of neurons to simulate and filter the output of each sub-network with the corresponding number of neurons.

[0022] The outputs of each selected sub-network are weighted and summed with the architecture selection weights to generate a unified approximate output with the same dimension as the outputs of all candidate network architectures. The specific expression is as follows:

[0023]

[0024] In the formula, m i Represents a tensor mask; This represents the summation result of different approximate neuron counts; x This represents the input to the hidden layer; M This represents the number of different learnable neurons; o max ( x The ) represents the calculated result of the maximum number of neurons; s i Indicates the weights for architecture selection;

[0025] By introducing an identity transformation, the input of the hidden layer is multiplied by the corresponding architecture selection weights, and then superimposed with the unified approximation output to finally form a continuously differentiable hidden layer output representation, as shown in the following expression:

[0026]

[0027] In the formula, s 0 Indicates the weights of the identity transformation; o continuous ( x ) represents the output representation of a continuously differentiable hidden layer.

[0028] Tensor mask architecture selection weights s i The specific calculation formula is as follows:

[0029]

[0030] In the formula, S i represents the continuous architecture parameter; exp() represents the exponential function e.

[0031] A two-layer optimization method is employed to collaboratively optimize the continuous architectural parameters and the network weight parameters of the network architecture itself in the differentiable learning space. Specifically, it includes an inner optimization layer and an outer optimization layer, wherein:

[0032] The inner optimization layer is used to optimize the network weight parameters and biases of the network architecture itself. w , b ;

[0033] The outer optimization layer is used to optimize the continuous architecture parameters of each tensor mask and identity transformation.S i ;

[0034] The specific expressions for the optimization processes of the inner and outer optimization layers are as follows:

[0035]

[0036] In the formula, w * , b * Bias respectively w , b The optimized value; α This is the proportionality coefficient; , represents the loss functions of the outer and inner optimization layers, respectively, both used to measure the degree to which the physical field variables output by the network satisfy the governing equations; st represents the constraint condition for minimizing the first optimization objective.

[0037] Based on the optimal continuous architecture parameters, the optimal network architecture in the discrete learning space is determined, specifically including:

[0038] Based on the optimal continuous architecture parameters obtained through collaborative optimization, the architecture selection weights in each hidden layer are extracted. s i and identity transformation weights s 0 The value;

[0039] For each hidden layer, select weights for each architecture. s i and identity transformation weights s 0 The values ​​are compared, and the configuration of the hidden layer is determined based on the weight with the largest weight value, as follows:

[0040] If the maximum weight is selected by any architecture, then the weight is chosen. s k , k ∈ i The hidden layer is then configured as a fully connected layer with multiple neurons, where the number of neurons is determined by the weights in the architecture. s k The corresponding architecture has been determined;

[0041] If the maximum weight is the weight of the identity transformation s 0 Then the configuration of the hidden layer is an identity transformation;

[0042] Repeat the process to determine the configuration of each hidden layer in turn, and integrate the configurations of each hidden layer to form the optimal network architecture.

[0043] Initialize the network weight parameters of the determined optimal network architecture, and train the optimal network architecture with the goal of minimizing the loss function. This includes the following steps:

[0044] Based on the final determined optimal network architecture, construct the continuously differentiable hidden layer output representations of each hidden layer in the optimal network architecture to form a new neural network.

[0045] For network weight parameters and biases w , b Perform random initialization;

[0046] Using the loss function as the training objective function, sampling points are uniformly selected in the computational domain, and the optimal network architecture is retrained until the number of training iterations reaches the preset upper limit or the loss function converges to a given threshold, thus completing the training of the optimal network architecture.

[0047] The beneficial effects of this invention are:

[0048] This invention constructs a loss function based on the control equation to establish a discrete learning space for learning network architecture, and performs continuous relaxation to obtain a differentiable learning space. A two-layer optimization method is then used to collaboratively optimize the continuous architecture parameters and the network weight parameters of the network architecture itself in the differentiable learning space, automatically learning to obtain the optimal network architecture. This effectively overcomes the limitations of traditional manual network architecture design, which relies excessively on human experience and requires repeated trial and error. It achieves automated design and optimization of network architecture, providing effective guidance for neural network structure design in arc plasma simulation and improving simulation accuracy and generalization ability. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a schematic diagram of the overall process of the electric arc plasma simulation method of the present invention;

[0051] Figure 2 This is a schematic diagram of the two-layer optimization method in an embodiment of the present invention;

[0052] Figure 3 This is a schematic diagram of the simulation results of the temperature distribution of the arc radius in an embodiment of the present invention;

[0053] Figure 4 This is a schematic diagram comparing the predicted temperature value with the reference value at 0.2ms in an embodiment of the present invention;

[0054] Figure 5 This is a schematic diagram comparing the predicted temperature value with the reference value at 0.6ms in an embodiment of the present invention;

[0055] Figure 6 This is a schematic diagram comparing the predicted temperature value with the reference value at time 1.0ms in an embodiment of the present invention. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] like Figures 1 to 6 As shown, an arc plasma simulation method based on a self-learning network architecture includes the following steps:

[0058] The simulation process is defined with the spatial coordinates and time of the electric arc plasma as input and the physical field variables determined by the electric arc plasma control equation as output.

[0059] A loss function is constructed based on the control equations of electric arc plasma to measure the degree to which physical field variables satisfy the control equations.

[0060] Using the loss function as a standard to measure the performance of the network architecture, a discrete learning space for learning the network architecture is constructed, and learnable continuous architecture parameters are introduced to continuously relax the discrete learning space to obtain a differentiable learning space.

[0061] With minimizing the loss function as the optimization objective, a two-layer optimization method is used to jointly optimize the continuous architecture parameters in the differentiable learning space and the network weight parameters of the network architecture itself, so as to obtain the optimal continuous architecture parameters.

[0062] Based on the optimal continuous architecture parameters, the optimal network architecture in the discrete learning space is determined;

[0063] Initialize the network weight parameters of the determined optimal network architecture, and train the optimal network architecture with the goal of minimizing the loss function;

[0064] The simulation process is executed using the optimal network architecture after training. By inputting spatial coordinates and time, the corresponding physical field variables are output to obtain the simulation results of electric arc plasma.

[0065] This invention constructs a loss function based on the control equation to establish a discrete learning space for learning network architecture, and performs continuous relaxation to obtain a differentiable learning space. A two-layer optimization method is then used to collaboratively optimize the continuous architecture parameters and the network weight parameters of the network architecture itself in the differentiable learning space, automatically learning to obtain the optimal network architecture. This effectively overcomes the limitations of traditional manual network architecture design, which relies excessively on human experience and requires repeated trial and error. It achieves automated design and optimization of network architecture, providing effective guidance for neural network structure design in arc plasma simulation and improving simulation accuracy and generalization ability.

[0066] Taking the one-dimensional electric arc Elenbaas-Heller equation with radial velocity terms as an example, the partial differential form of the electric arc plasma control equation is expressed as follows:

[0067]

[0068] In the formula, ρ Mass density; v r Radial velocity; C p Specific heat; T It is the arc temperature; r Radial distance; κ Thermal conductivity; σ Electrical conductivity; I For current; g c Arc conductivity; E rad Energy dissipation due to radiative transport; t set For the maximum time; R Let be the radius of the electric arc; where, the parameter t set , R Temperature boundary conditions need to be set directly; ρ , C p , κ , σ , E rad These parameters are determined by the gas, gas pressure, and arc temperature that generate the arc; Indicates time t Perform differentiation; This indicates taking the derivative with respect to the radial distance;

[0069] Temperature of the network architecture and radial velocity Substituting the terms into the partial differential form of the governing equation and moving the entire equation to the left side of the equation, let the terms on the left side of the equation be denoted as . The loss function is designed as follows:

[0070]

[0071] In the formula, L For loss function, N The number of sampling points is given. If initial and boundary conditions exist, the complete loss function can be obtained by summing them with the above formula in the same form.

[0072] The discrete learning space includes a variety of candidate network architectures, which are formed by combinations of different numbers of hidden layers and different numbers of neurons within each hidden layer.

[0073] The number of hidden layers in the network architecture ranges from 1 to 5, and the number of neurons in each hidden layer ranges from 50 to 500.

[0074] Introducing learnable continuous architecture parameters to continuously relax the discrete learning space, specifically including:

[0075] Assign optimizable continuous architecture parameters to the network architecture for each configuration in the discrete learning space;

[0076] Generate a tensor mask consisting of 1s and 0s for the hidden layer in each network architecture configuration;

[0077] The continuous architecture parameters are converted into architecture selection weights for the corresponding tensor mask using differentiable functions;

[0078] Based on the architecture selection weights, the outputs of each masked network architecture are weighted and combined to generate a continuously differentiable hidden layer output representation, thus completing the continuous relaxation process.

[0079] The weighted combination of the masked network architecture outputs based on architecture selection weights is performed through architecture approximation units, specifically including:

[0080] The tensor mask is multiplied by the computation result of the hidden layer with the largest number of neurons to simulate and filter the output of each sub-network with the corresponding number of neurons.

[0081] The outputs of each selected sub-network are weighted and summed with the architecture selection weights to generate a unified approximate output with the same dimension as the outputs of all candidate network architectures. The specific expression is as follows:

[0082]

[0083] In the formula, m i Represents a tensor mask; This represents the summation result of different approximate neuron counts; x This represents the input to the hidden layer;M This represents the number of different learnable neurons; o max ( x The ) represents the calculated result of the maximum number of neurons; s i Indicates the weights for architecture selection;

[0084] By introducing an identity transformation, the input of the hidden layer is multiplied by the corresponding architecture selection weights, and then superimposed with the unified approximation output to finally form a continuously differentiable hidden layer output representation, as shown in the following expression:

[0085]

[0086] In the formula, s 0 Indicates the weights of the identity transformation; o continuous ( x ) represents the output representation of a continuously differentiable hidden layer.

[0087] Tensor mask architecture selection weights s i The specific calculation formula is as follows:

[0088]

[0089] In the formula, S i represents the continuous architecture parameter; exp() represents the exponential function e.

[0090] A two-layer optimization method is employed to collaboratively optimize the continuous architectural parameters and the network weight parameters of the network architecture itself in the differentiable learning space. Specifically, it includes an inner optimization layer and an outer optimization layer, wherein:

[0091] The inner optimization layer is used to optimize the network weight parameters and biases of the network architecture itself. w , b ;

[0092] The outer optimization layer is used to optimize the continuous architecture parameters of each tensor mask and identity transformation. S i ;

[0093] The specific expressions for the optimization processes of the inner and outer optimization layers are as follows:

[0094]

[0095] In the formula, w * , b * Bias respectively w ,b The optimized value; α This is the proportionality coefficient; , represents the loss functions of the outer and inner optimization layers, respectively, both used to measure the degree to which the physical field variables output by the network satisfy the governing equations; st represents the constraint condition for minimizing the first optimization objective.

[0096] Based on the optimal continuous architecture parameters, the optimal network architecture in the discrete learning space is determined, specifically including:

[0097] Based on the optimal continuous architecture parameters obtained through collaborative optimization, the architecture selection weights in each hidden layer are extracted. s i and identity transformation weights s 0 The value;

[0098] For each hidden layer, select weights for each architecture. s i and identity transformation weights s 0 The values ​​are compared, and the configuration of the hidden layer is determined based on the weight with the largest weight value, as follows:

[0099] If the maximum weight is selected by any architecture, then the weight is chosen. s k , k ∈ i The hidden layer is then configured as a fully connected layer with multiple neurons, where the number of neurons is determined by the weights in the architecture. s k The corresponding architecture has been determined;

[0100] If the maximum weight is the weight of the identity transformation s 0 Then the configuration of the hidden layer is an identity transformation;

[0101] Repeat the process to determine the configuration of each hidden layer in turn, and integrate the configurations of each hidden layer to form the optimal network architecture.

[0102] Initialize the network weight parameters of the determined optimal network architecture, and train the optimal network architecture with the goal of minimizing the loss function. This includes the following steps:

[0103] Based on the final determined optimal network architecture, construct the continuously differentiable hidden layer output representations of each hidden layer in the optimal network architecture to form a new neural network.

[0104] For network weight parameters and biases w , b Perform random initialization;

[0105] Using the loss function as the training objective function, sampling points are uniformly selected in the computational domain, and the optimal network architecture is retrained until the number of training iterations reaches the preset upper limit or the loss function converges to a given threshold, thus completing the training of the optimal network architecture.

[0106] In this embodiment, inner-layer optimization and outer-layer optimization are performed alternately, such as... Figure 2 As shown, specifically:

[0107] At the start of training, the weights and biases of the inner optimization network are randomly initialized. w , b And the continuous architecture parameters of the tensor mask and identity transformation. S i Initialize all layers to 0, and use two independent Adam optimizers to optimize the inner and outer layers. The learning rate of the inner optimizer is set to 10. -3 After every 100,000 inner-layer optimizations, the learning rate decreases to half its original value; the learning rate of the outer-layer optimizer is set to 10. -4 The optimization does not decay. An outer layer optimization is performed once every 10 iterations of inner layer optimization, for a total of 50,000 outer layer optimizations.

[0108] After each inner-layer optimization, it is checked whether the number of inner-layer optimizations is a multiple of 10. If the result is no, inner-layer optimization continues, iterating and updating continuously. If the result is yes, outer-layer optimization begins, optimizing the continuous architecture parameters of the tensor mask and identity transformation. S i ;

[0109] After each outer layer optimization, check if the number of outer layer optimizations has reached 50,000. If the result is no, repeat the inner layer optimization. If the result is yes, training ends.

[0110] When the maximum number of optimization steps is reached, the tensor mask weights of each hidden layer are determined based on the self-learning results. s i and identity transformation weights s The value of 0, the number of neurons corresponding to the weight with the largest retained value, and the expression represented by the output of the hidden layer are combined to form the final self-learning network architecture of the hidden layer.

[0111] The computational representations of each hidden layer are constructed based on the expressions of the hidden layer outputs, forming a new neural network. A random seed, identical to that used in the self-learning process, is selected, and the network weight parameters and biases are adjusted. w , b Perform random initialization, retrain until the loss function converges, and plot the final solved arc temperature and radial velocity distributions, as shown below. Figure 3As shown, the temperature distribution along the arc radius from 0 ms to 1 ms is presented. Figure 3 The simulation intuitively reflects the temperature evolution behavior of the electric arc plasma in both time and space, demonstrating that the network architecture trained in this application can effectively capture the dynamic thermal characteristics of the electric arc, and the simulation results show a reasonable physical distribution trend; for example... Figure 4 , Figure 5 , Figure 6 As shown, the temperature prediction values ​​are compared with the reference values ​​at 0.2ms, 0.6ms, and 1.00ms, respectively. The prediction curves and reference curves in each figure are in high agreement, indicating that the simulation method of this application maintains high simulation accuracy and stability during the time progression.

[0112] Using the solution of the high-order boundary value problem solver as a reference, the simulation results of the self-learning network architecture are compared with the simulation results of the manually designed network architecture. The results are shown in Table 1. The results in the table show that the network architecture obtained by self-learning according to the method proposed in this invention can effectively reduce the prediction error caused by the manually designed network and improve the prediction accuracy by an order of magnitude.

[0113] Table 1 Comparison of L2 norm errors

[0114]

[0115] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0116] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claims.

Claims

1. A method for simulating electric arc plasma based on a self-learning network architecture, characterized in that, Includes the following steps: The simulation process is defined with the spatial coordinates and time of the electric arc plasma as input and the physical field variables determined by the electric arc plasma control equation as output. A loss function is constructed based on the control equations of electric arc plasma to measure the degree to which physical field variables satisfy the control equations. Using the loss function as a standard to measure the performance of the network architecture, a discrete learning space for learning the network architecture is constructed, and learnable continuous architecture parameters are introduced to continuously relax the discrete learning space to obtain a differentiable learning space. With minimizing the loss function as the optimization objective, a two-layer optimization method is used to jointly optimize the continuous architecture parameters in the differentiable learning space and the network weight parameters of the network architecture itself, so as to obtain the optimal continuous architecture parameters. Based on the optimal continuous architecture parameters, the optimal network architecture in the discrete learning space is determined; Initialize the network weight parameters of the determined optimal network architecture, and train the optimal network architecture with the goal of minimizing the loss function; The simulation process is executed using the optimal network architecture after training. By inputting spatial coordinates and time, the corresponding physical field variables are output to obtain the simulation results of electric arc plasma. The discrete learning space includes a variety of candidate network architectures, which are formed by a combination of different configurations of the number of hidden layers and different configurations of the number of neurons in each hidden layer. Introducing learnable continuous architecture parameters to continuously relax the discrete learning space, specifically including: Assign optimizable continuous architecture parameters to the network architecture for each configuration in the discrete learning space; Generate a tensor mask consisting of 1s and 0s for the hidden layer in each network architecture configuration; The continuous architecture parameters are converted into architecture selection weights for the corresponding tensor mask using differentiable functions; Based on the architecture selection weights, the outputs of each masked network architecture are weighted and combined to generate a continuously differentiable hidden layer output representation, thus completing the continuous relaxation process. A two-layer optimization method is employed to collaboratively optimize the continuous architectural parameters and the network weight parameters of the network architecture itself in the differentiable learning space. Specifically, it includes an inner optimization layer and an outer optimization layer, wherein: The inner optimization layer is used to optimize the network weight parameters and biases of the network architecture itself. w , b ; The outer optimization layer is used to optimize the continuous architecture parameters of each tensor mask and identity transformation. S i ; The specific expressions for the optimization processes of the inner and outer optimization layers are as follows: In the formula, w , b Bias respectively w , b The optimized value; α This is the proportionality coefficient; , represents the loss function of the outer optimization layer and the inner optimization layer, respectively, both used to measure the degree to which the physical field variables output by the network satisfy the governing equations; st represents the constraint condition for minimizing the first optimization objective. M This represents the number of different learnable neurons; s i This indicates the weights for architecture selection.

2. The arc plasma simulation method based on a self-learning network architecture according to claim 1, characterized in that, The weighted combination of the masked network architecture outputs based on architecture selection weights is performed through architecture approximation units, specifically including: The tensor mask is multiplied by the computation result of the hidden layer with the largest number of neurons to simulate and filter the output of each sub-network with the corresponding number of neurons. The outputs of each selected sub-network are weighted and summed with the architecture selection weights to generate a unified approximate output with the same dimension as the outputs of all candidate network architectures. The specific expression is as follows: In the formula, m i Represents a tensor mask; This represents the summation result of different approximate neuron counts; x This represents the input to the hidden layer; o max ( x The ) represents the calculated result of the maximum number of neurons; By introducing an identity transformation, the input of the hidden layer is multiplied by the corresponding architecture selection weights, and then superimposed with the unified approximation output to finally form a continuously differentiable hidden layer output representation, as shown in the following expression: In the formula, s 0 indicates the weight of the identity transformation; o continuous ( x ) represents the output representation of a continuously differentiable hidden layer.

3. The arc plasma simulation method based on a self-learning network architecture according to claim 2, characterized in that, Tensor mask architecture selection weights s i The specific calculation formula is as follows: In the formula, S i represents the continuous architecture parameter; exp() represents the exponential function e.

4. The arc plasma simulation method based on a self-learning network architecture according to claim 1, characterized in that, Based on the optimal continuous architecture parameters, the optimal network architecture in the discrete learning space is determined, specifically including: Based on the optimal continuous architecture parameters obtained through collaborative optimization, the architecture selection weights in each hidden layer are extracted. s i and identity transformation weights s 0 The value; For each hidden layer, select weights for each architecture. s i and identity transformation weights s 0 The values ​​are compared, and the configuration of the hidden layer is determined based on the weight with the largest weight value, as follows: If the maximum weight is selected by any architecture, then the weight is chosen. s k , k ∈ i The hidden layer is then configured as a fully connected layer with multiple neurons, where the number of neurons is determined by the weights in the architecture. s k The corresponding architecture has been determined; If the maximum weight is the weight of the identity transformation s 0 Then the configuration of the hidden layer is an identity transformation; Repeat the process to determine the configuration of each hidden layer in turn, and integrate the configurations of each hidden layer to form the optimal network architecture.

5. The arc plasma simulation method based on a self-learning network architecture according to claim 4, characterized in that, Initialize the network weight parameters of the determined optimal network architecture, and train the optimal network architecture with the goal of minimizing the loss function. This includes the following steps: Based on the final determined optimal network architecture, construct the continuously differentiable hidden layer output representations of each hidden layer in the optimal network architecture to form a new neural network. For network weight parameters and biases w , b Perform random initialization; Using the loss function as the training objective function, sampling points are uniformly selected in the computational domain, and the optimal network architecture is retrained until the number of training iterations reaches the preset upper limit or the loss function converges to a given threshold, thus completing the training of the optimal network architecture.

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